通过相对Krasnoselskii-Mann迭代求解不可约随机平均收益博弈与熵博弈
Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration
AI总结：
本研究结合相对值迭代与Krasnoselskii-Mann阻尼提出求解不可约随机平均收益博弈的算法，证明其ε-近似迭代复杂度为O(|logε|)，还将方法拓展至熵博弈并通过变分分析验证收缩性质。
摘要：
我们分析了一种求解随机平均收益博弈的算法，该算法结合了相对值迭代与Krasnoselskii-Mann阻尼的思想。我们针对满足不可约条件的多类博弈推导出了参数化复杂度界。我们特别证明，不可约并发随机博弈的值的ε-近似值可通过O(|logε|)次迭代计算得出，其中O(·)中的常数是显式的，取决于最小的非零转移概率。这一结果可与Chatterjee和Ibsen-Jensen（ICALP 2014）针对同类博弈得到的O(|ε|^{-1}|log(ε)|)界，以及Allamigeon、Gaubert、Katz和Skomra（ICALP 2022）针对回合制博弈得到的O(|ε|^{-1})界进行对比。我们还为熵博弈——一类由Asarin、Cervelle、Degorre、Dima、Horn和Kozyakin提出的矩阵乘法博弈——建立了参数化复杂度界。我们通过变分分析方法得到这些结果，证明了相对Krasnoselskii-Mann迭代关于Hilbert半范数的收缩性质。
英文摘要：
We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an $ε$-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in $O(|\logε|)$ where the constant in the $O(\cdot)$ is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in $O(|ε|^{-1}|\log(ε)|)$ obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a $O(|ε|^{-1})$ bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert's semi-norm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
